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人気のある微分積分 >

limit as y approaches infinity of (3+2/(y^3)-3y^4)/(9y^4-5/(y^2)-3)

解

y \to \infty lim (\frac{3 + \frac{2}{y ^{3}} - 3 y ^{4}}{9 y ^{4} - \frac{5}{y ^{2}} - 3})

解

- \frac{1}{3}

+1

十進法表記

- 0.33333 \dots

解答ステップ

y \to \infty lim (\frac{3 + \frac{2}{y ^{3}} - 3 y ^{4}}{9 y ^{4} - \frac{5}{y ^{2}} - 3})

拡張

\frac{3 + \frac{2}{y ^{3}} - 3 y ^{4}}{9 y ^{4} - \frac{5}{y ^{2}} - 3} : \frac{3 y ^{3} + 2 - 3 y ^{7}}{9 y ^{7} - 3 y ^{3} - 5 y}

= y \to \infty lim (\frac{3 y ^{3} + 2 - 3 y ^{7}}{9 y ^{7} - 3 y ^{3} - 5 y})

最高の分母べき乗で割る:

\frac{\frac{3}{y ^{4}} + \frac{2}{y ^{7}} - 3}{9 - \frac{3}{y ^{4}} - \frac{5}{y ^{6}}}

= y \to \infty lim (\frac{\frac{3}{y ^{4}} + \frac{2}{y ^{7}} - 3}{9 - \frac{3}{y ^{4}} - \frac{5}{y ^{6}}})

x \to a lim [\frac{f ( x )}{g ( x )}] = \frac{lim _{x \to a} f ( x )}{lim _{x \to a} g ( x )}, x \to a lim g (x) \neq = 0

不定形式の場合を除く

= \frac{lim _{y \to \infty} ( \frac{3}{y ^{4}} + \frac{2}{y ^{7}} - 3 )}{lim _{y \to \infty} ( 9 - \frac{3}{y ^{4}} - \frac{5}{y ^{6}} )}

y \to \infty lim (\frac{3}{y ^{4}} + \frac{2}{y ^{7}} - 3) = - 3

y \to \infty lim (9 - \frac{3}{y ^{4}} - \frac{5}{y ^{6}}) = 9

= \frac{- 3}{9}

簡素化

\frac{- 3}{9} : - \frac{1}{3}

= - \frac{1}{3}

グラフ

人気の例

limit as x approaches infinity of (3x+1)/(sqrt(4x^2-3x-7))

x \to \infty lim (\frac{3 x + 1}{4 x ^{2} - 3 x - 7})

limit as x approaches 4 of x^2+3x-4

x \to 4 lim (x^{2} + 3 x - 4)

limit as x approaches 0 of 4x^{7x}

x \to 0 lim (4 x^{7 x})

limit as x approaches 0 of ln(x^x)

x \to 0 lim (ln (x^{x}))

limit as x approaches-infinity of x,4

x \to - \infty lim (x, 4)